Radians

• What unit is more convenient for measuring angular displacement in circular motion?

  Radians
• How is angular displacement (θ) defined in circular motion?

  Change in angle in radians during rotation
• What is the ratio that defines angular displacement?

  Arc length to radius of the circle
• What must be true about the distances used to calculate angular displacement?

  Both must be in the same units
• How is a radian (rad) defined?

  Angle subtended by an arc equal to radius

  
• How can angular displacement be calculated?

  Using the ratio of arc length to radius
• When the angle is one radian, what is the relationship between arc length and radius?

  Arc length equals the radius

  
• What does $\Delta\theta$ represent in circular motion?


  Angular displacement in radians
• What does $s$ represent in the context of circular motion?


  Length of the arc in meters
• What does $r$ represent in circular motion?


  Radius of the circle in meters
• How is the angle in radians for a complete circle expressed?

  Equal to $2\pi$ radians

  
• How do you convert radians to degrees?

  Multiply by $\frac{180}{\pi}$

  
• How do you convert degrees to radians?

  Multiply by $\frac{\pi}{180}$

  
• What are the common conversions from degrees to radians?

  • 0° = 0 rad
  • 90° = $\frac{\pi}{2}$ rad
  • 180° = $\pi$ rad
  • 270° = $\frac{3\pi}{2}$ rad
  • 360° = $2\pi$ rad

  
• What should you check on your calculator when using trigonometric functions?

  Ensure it's in the correct mode (Deg or Rad)
• Why is it important to use the correct calculator mode for trigonometric functions?

  To avoid incorrect answers and lost marks
• Which trigonometric functions require the calculator mode to be checked?

  Sin, cos, and tan
• What are the consequences of using the wrong calculator mode?

  • Incorrect answers
  • Loss of marks
  • Confusion in calculations